Utterly Mad

Just gonna put this out there, but IRL 7.62x24 would be a ridiculously anemic round, with performance closer to that of a pistol round than a proper rifle cartridge. The closest real world equivalent to it (7.62x25) has a muzzle velocity of about 1800 FPS out of a submachine gun barrel using an 85 grain bullet. At 1800 meters, assuming you could angle the gun that much while still accurately shooting, you'd literally be able to deflect the thing with a loose bedsheet.

It might be nitpicky, but something TRULY magical would have to happen to propellant design to change that while still maintaining such small dimensions. Given that we're only 20 or 30 years ahead of present from my understanding, and evolution in ballistic weapons is typically pretty slow, that seems pretty unlikely to have happened.

As a solution, I'd just suggest making it bigger. Spec it out as a non-belted, rimless 7.62 calibre, with a 57mm case that is roughly 14mm wide, give it a steep shoulder and a very slight taper, and you have a fairly short (little bigger than .308) cartridge that will feed well in a semi-auto and reliably kill stuff out to 1000 meter with even today's powders. Run it at a very high pressure, and you can stretch that out pretty well. Say your gun is innovatively designed to eat the kick (because it would certainly be present), and there you go. Put a 150 grain bullet in it, and you have a good MG cartridge, and put a sleeker but heavier 180 odd grain bullet in it and you have a good sniper round.

The RAHEAD is a bit more sound, but 5000 meters (I mean, that's 5 KILOMETERS, which depending on where you are is beyond the horizon point) is pretty far, and when rocket assisted ammo has been tested IRL, it's been proven to perform better at medium distance than short or long. Being as it's less based in IRL tech, I have very little to offer in terms of suggestions regarding it.

/2 cents.